Weibull Radar Clutter (Radar, Sonar, Navigation and Avionics Series, 3)

212 Pages·1990·7.05 MB·English

by  Matsuo Sekine

WEIBULL
RADAR
CLUTTER
Matsuo Sekine
& Yuhai Mao
Peet r Peergnirus Ldt . on behalf of ht e nIsutitoit n of Eelccrtial Engnieers
Published by: Peter Peregrinus Ltd., London, United Kingdom
© 1990: Peter Peregrinus Ltd.
Apart from any fair dealing for the purposes of research or private study,
or criticism or review, as permitted under the Copyright, Designs and
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While the authors and the publishers believe that the information and
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disclaimed.
British Library Cataloguing in Publication Data
Sekine, Matsuo, 1945-
Weibull radar clutter.
1. Radar
I. Title II. Mao, Y. H.
621.3848
ISBN 0 86341 191 6
Printed in England by BPCC Wheatons Ltd., Exeter
P r e f a ce
Radar clutter is defined as the unwanted reflective waves from irrelevant
targets. The amplitude statistics of clutter have been modelled by Rayleigh,
log-normal, contaminated-normal, Weibull, log-Weibull and ^-distributions.
During the past twenty years there has been a considerable growth of
interest in various Weibull-distributed ground, sea, sea ice and weather clutter
returns concerning false alarms and effective detection processes.
In the opening chapter, the reader is introduced to the derivation of Weibull
distribution in a general way. Chapter 2 deals with radar clutter as statistics
with Weibull distribution.
As with signal detection methods in clutter, parametric constant false alarm
rate (CFAR) detectors in Weibull clutter and non-parametric CFAR detec-
tors are dealt with in Chapter 3.
The suppression of radar clutter is a very important problem in modern
radar technology. There are many papers and books discussing this problem.
We do not discuss this problem in general, but discuss some special problems
concerning Weibull clutter, these subjects being covered in Chapter 4 and the
Appendixes.
This comprehensive work should prove invaluable, not only to radar
engineers, but also to all who are in any way concerned with Weibull
distribution.
During the preparation of the manuscript, we recorded, with deep regret,
the death in November 1988 of Dr John Clarke of the Institution of Electrical
Engineers and the Royal Signals and Radar Establishment of the United
Kingdom, who encouraged us to write this book. We should like to dedicate
this book to his memory.
The manuscript as prepared while Yuhai Mao was with the Department of
Applied Electronics at the Tokyo Institute of Technology in Japan, and
Matsuo Sekine was with the Department of Electromagnetic Theory at the
Royal Institute of Technology in Sweden.
We had the benefit of lengthy discussions with a number of colleagues and
friends in Japan, The People's Republic of China, and Sweden. We thank, in
particular, Prof. Toshimitsu Musha of the Tokyo Institute of Technology,
Prof. Yoshiwo Okamoto of Chiba Institute of Technology, Prof. Zhao-Da
Zhu of Nanjing Institute of Aeronautics, Prof. Zai-Gen Fang of Beijing
Institute of Technology, Prof. Staffan Strom of the Royal Institute of Tech-
nology, and the late Prof. Goran Lind and Prof. Gerhard Kristensson of
Lund Institute of Technology, for their valuable suggestions.
Finally, the permission by the various journals to reproduce the material
here is gratefully acknowledged.
Matsuo Sekine
Yuhai Mao
I n t r o d u c t i on
There are two kinds of radar echo. One is the echo signal reflected from the
targets which we are interested in, such as aircrafts, ships, guided missiles etc.
The other is the echo signal reflected from unrelated bodies, such as land,
clouds, rain, snow, sea waves, birds, insects and angels (atmospheric turbu-
lence). However, 'useful' signal is meant simply in the relative sense. The
useful signal for some applications may become the harmful signal in another
case. For example, the echo signal from clouds is useful for weather radar, but
is harmful for most other radars. In general, the background echo, which is
termed 'clutter', is harmful for most radars. The useful target signal is often
embedded in the clutter. Therefore, how to suppress clutter and to detect
target signals from the clutter is one of the most important problems in
modern radar technology.
First, we have to study the statistical properties of the clutter echo. These
are very complex. They not only depend on the type of background, but also
on the parameters of the radar, such as resolution, wavelength, polarisation
etc. Since the environment will change with time, the clutter signal also
exhibits non-stationary statistics. This adds more complexity to the study of
statistical properties of clutter.
Thus we have to search for methods for clutter suppression. Since the
statistical properties of clutter for different environments are different, the
methods of suppression will be also different for different types of clutter. For
example, an ordinary MTI system is sufficient for the suppression of ground
clutter, but is ineffective for suppression of weather clutter, sea clutter, or
other moving clutter. Adaptive MTI systems are effective for most forms of
clutter and they can track the variation of the clutter spectrum. However, a
good adaptive MTI system design also implies knowledge of the statistical
properties of the clutter.
There are many kinds of characteristics which describe the properties of
radar clutter. The principal ones are relative intensity, amplitude distribution,
autocorrelation functions, in time and in space, spectrum, polarisation proper-
ties etc. All depend on the specification of the radar, especially the wavelength
of the resoluton cell (i.e. the pulse width and the beamwidth) of the radar, and
grazing angle, on one hand; and on the type of the clutter, such as land,
weather, sea and chaff etc, on the other.
We often use the backscatter coefficient a to represent the relative intensity
0
of the clutter. The radar cross-section of the clutter can be calculated from this
coefficient and the resolution cell of the radar. It can be calculated for low
grazing angles from
(1)
where R is the distance from clutter to radar, A0 is the azimuth beamwidth of
the radar, c is the velocity of light, and T is the pulse width of the radar.
Decreasing the size of resolution can decrease the intensity of clutter signal.
The mean backscatter coefficient depends mainly on the type of clutter. The
largest is for land clutter, next comes sea clutter and then weather clutter. In
the case of land clutter, it depends on the type of terrain. This ranks as
follows: cities, mountains, small house districts, wooded hills, open woods,
cultivated land and desert. The median backscatter coefficient increases some-
what with frequency for most terrain types, but usually not more than linear
with transmit frequency. The median backscatter coefficient increases about
linearly with depression angle from 0-5° to 10° below the horizontal.
Since the clutter signal is not a steady signal, it fluctuates with time and
space. Therefore, it is better to consider the clutter signal as being a random
sequence, and to study its statistical properties.
The most important property may be the amplitude distribution of clutter.
This has been described using Rayleigh model assumptions for many years.
The reason for this is the mathematical simplicity of computation and the lack
of knowledge of real clutter. However, as the size of the resolution cell of the
radar decreases, the clutter distribution develops a larger tail than the
Rayleigh distribution. Consequently, if the Rayleigh model is still used, the
predicted false-alarm probability will be incorrect, and the CFAR detector
based on this assumption cannot maintain the false-alarm rate constant in real
clutter conditions.
Recent investigations of natural clutter characteristics have shown that the
clutter echo can be approximated by a Weibull distribution. It is noteworthy
that the Rayleigh distribution is a special case of the Weibull distribution
family. The truth of the Weibull distribution reported first in land clutter
returns as seen by high-resolution radars, and the skewness of the Weibull
distribution was shown to increase as the radar depression angle was de-
creased [I]. Recently, Weibull distribution has also been observed in weather
clutter [2] and sea clutter [3], These facts are the principal motivation for the
use of the Weibull clutter model.
Weibull distribution was proposed by a Swedish Professor, Waloddi
Weibull, in 1939 [4] to establish a statistical theory of the strength of
materials. Up to 1977, more than 1000 books and papers had been published
on the theoretical properties of the distribution, its use for the statistical
analysis of test data, and its practical applications [5].
The Weibull distribution is given by
(2)
otherwise
where a and rj are the scale and shape parameters, respectively. For rj = 2 we
get the Rayleigh distribution
(3)
Some examples of the Weibull distribution are plotted in Fig. 1, where a = 1.
We can see from this Figure that the Weibull distribution with r\ < 2 has a
larger tail than the Rayleigh distribution (rj = 2).
However, clutter as seen from a fixed point varies both in time at a given
range and spatially. Spatial and temporal distributions are generally different.
This means that the data collected from a fixed area has a distribution which
differs from that collected from different regions. In practice, the former
corresponds to the tracking radar, and the latter corresponds to the search
radar with a scanning antenna. For land clutter, temporal distributions
(observed spatial grid or footprint fixed) are usually considered to be Rician.
y
x
Fig. 1 Weibull distribution function
But some authors have reported that the temporal distributions for trees
between 9-5 and 95 GHz has log-normal shape and sometimes Weibull shape.
Reported spatial distributions for land extend from the Rayleigh to large
standard deviation log-normal and Weibull distributions.
Since Weibull distribution is a very flexible distribution, one can change its
shape by means of changes in the shape parameter. So it can be fitted to many
different types of clutter. In fact, clutter reflected from a specified area may
change its shape parameter not only with the resolution of the radar, but also
with time for a given radar. For example, sea clutter will change its shape
parameter as the wind speed changes [3]. In general, the shape parameter will
decrease as wind-speed increases. So we can use the Weibull distribution with
a wind-dependent shape parameter conveniently to describe sea clutter. This is
the reason why the Weibull distribution has been widely accepted.
The clutter signals are correlated in space, both in range direction and in
azimuth direction. In general, the correlation area corresponds to the resolu-
tion cell. This means that the correlation time in the range direction corre-
sponds to the pulse width; and in the azimution direction it corresponds to the
beamwidth. However, in the azimuth direction, since the antenna scanning
time for one beamwidth will occupy 10 to 20 pulse repetition periods, the
clutter may fluctuate in this time period. Therefore, the correlation time of
clutter in the azimuth direction is often less than the time needed for the
antenna scanning the beamwidth.
It is better to describe the fluctuation of the clutter in time with its
spectrum. The spectrum of the clutter can not only describe the speed of
fluctuation but also can reveal the Doppler frequency of the moving clutter.
This is very useful for the design of adaptive clutter cancellers in the frequency
domain.
In this book we will begin with the introduction of the fundamental
principle of the Weibull distribution and its applications. Then, we provide a
summary of the measured data of land clutter, weather clutter and sea clutter,
which can be modelled with the Weibull distribution. After describing the
detection problems in Weibull clutter, we discuss the methods of suppression
of Weibull clutter.
References
1 BOOTHE, R. R.: The Weibull distribution applied to the ground clutter backscatter co-
efficient', US Army Missile Command, Technical Report, RE-TR-69-15, AD A691109, 1969
2 SEKINE, M., MUSHA, T., TOMITA, Y., HAGISAWA, T., IRABU, T. and KIUCHI, E.:
4On Weibull distributed weather clutter', IEEE Trans., 1979, AES-15, pp. 824-830.
3 FAY, F. A., CLARKE, J. and PETERS, R. S.: 'Weibull distribution applied to sea clutter',
Radar 77, 1977, pp. 101-104.
4 WEIBULL, W.: 'A statistical theory of strength of materials'. I.V.A.-Handl. No. 151, 1939.
5 WEIBULL, W.: 'References on the Weibull distribution'. FTI A report, A20:23, Aug. 1977.
Contents
Preface ............................................................................... vii
Introduction ......................................................................... ix
References ................................................................................ xii
1. Fundamentals of Weibull Distribution ....................... 1
References ................................................................................ 3
2. Radar Clutter as Statistics with Weibull
Distribution .................................................................. 4
2.1 Land Clutter ....................................................................... 7
2.2 Sea Clutter ........................................................................ 19
2.3 Sea-ice Clutter ................................................................... 38
2.4 Weather Clutter ................................................................. 43
2.5 References ........................................................................ 47
3. Signal Detection in Weibull Clutter ............................ 49
3.1 False-alarm Probability in Weibull Clutter ......................... 50
3.2 CFAR Detector for Weibull Clutter .................................... 51
3.3 Non-parametric CFAR Detector ........................................ 79
3.4 Signal Detection in Weibull Clutter ................................... 87
3.4.1 Detection Performance of Linear Receiver
in Weibull Clutter ............................................... 89

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vi Contents
3.4.2 Detection Performance of a Logarithmic
Receiver in Weibull Clutter ................................ 89
3.4.3 Detection Performance of Binary Integrator
in Weibull Clutter ............................................... 95
3.4.4 Detection Performance of Median Detector
in Weibull Clutter ............................................... 96
3.4.5 Chernoff Bound of Optimum Performance ........ 98
3.5 Detection Performance of CFAR Detector in
Weibull Clutter ................................................................... 113
3.5.1 CFAR Loss of Log t Test ................................... 114
3.5.2 Detection Performance of Non-parametric
CFAR Detector .................................................. 114
3.6 References ........................................................................ 123
4. Suppression of Weibull Clutter .................................. 126
4.1 Introduction ........................................................................ 126
4.2 Suppression of Weibull Clutter in Time Domain ............... 129
4.2.1 Suppression of Clutter within a Single
Sweep ............................................................... 129
4.2.2 Suppression of Clutter within a Single Scan
(Multiple Sweeps) ............................................. 130
4.2.3 Suppression of Clutter within Multiple
Scans ................................................................ 140
4.3 Suppression of Weibull Clutter in Frequency
Domain .............................................................................. 141
4.3.1 Detector for Target Signal Known a Priori
Embedded in Weibull Clutter ............................. 146
4.3.2 Detector for Partially Fluctuaing Target in
Coherent Weibull Clutter ................................... 153

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